Algebraic Manipulation Worksheets With Answers - Craven Community College Page 5
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29E
P
XPONENTS AND
OLYNOMIALS
Integer Exponents
The following properties are used to work with exponents.
A
B
A+B
X
X
= X
To multiply with the same base you add exponents
A
A – B
X
= X
To divide with the same base you subtract exponents
B
X
A
A
A
(XY)
= X
Y
Exponents distribute over multiplication
A
B
AB
(X
)
= X
A power to a power is the product of the powers
-A
X
= 1
Negative exponents imply reciprocals
A
X
5
3
3
3
Example 1:
(XY
Z
)(X
Y
Z)
4
8
4
X
Y
Z
Add exponents for like bases
2
3
Example 2:
(2X
)
3
6
2
X
Multiple Exponents
6
8X
12
Example 3:
8X
9
12X
12 – 9
8 X
Divide the numerical coefficients
12
Subtracts the exponents on the variables
3
2X
Simplify
3
3
-2
Example 4:
A
B
-5
4
A
B
3
5
A
A
Make all exponents positive
2
4
B
B
8
A
Add exponents for the like bases
6
B
5
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